Vector Lyapunov functions and stability analysis of nonlinear systems:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
1991
|
| Series: | Mathematics and its applications
63 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 172 S. |
| ISBN: | 0792311523 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV004725111 | ||
| 003 | DE-604 | ||
| 005 | 20090810 | ||
| 007 | t| | ||
| 008 | 920226s1991 xx |||| 00||| engod | ||
| 020 | |a 0792311523 |9 0-7923-1152-3 | ||
| 035 | |a (OCoLC)23144362 | ||
| 035 | |a (DE-599)BVBBV004725111 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-91G |a DE-739 |a DE-355 |a DE-19 |a DE-634 |a DE-11 |a DE-188 | ||
| 050 | 0 | |a QA871 | |
| 082 | 0 | |a 003/.75 |2 20 | |
| 084 | |a SK 520 |0 (DE-625)143244: |2 rvk | ||
| 084 | |a MAT 345f |2 stub | ||
| 100 | 1 | |a Lakshmikantham, Vangipuram |d 1926-2012 |e Verfasser |0 (DE-588)104268050 |4 aut | |
| 245 | 1 | 0 | |a Vector Lyapunov functions and stability analysis of nonlinear systems |c by V. Lakshmikantham, V. M. Matrosov and S. Sivasundaram |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1991 | |
| 300 | |a X, 172 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 63 | |
| 650 | 7 | |a Liapounov, fonctions de |2 ram | |
| 650 | 7 | |a Stabilité |2 ram | |
| 650 | 7 | |a Théories nonlinéaires |2 ram | |
| 650 | 4 | |a Lyapunov functions | |
| 650 | 4 | |a Nonlinear theories | |
| 650 | 4 | |a Stability | |
| 650 | 0 | 7 | |a Nichtlineares System |0 (DE-588)4042110-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Ljapunov-Funktion |0 (DE-588)4274502-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Vektorwertige Funktion |0 (DE-588)4262911-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Ljapunov-Stabilitätstheorie |0 (DE-588)4167992-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Ljapunov-Funktion |0 (DE-588)4274502-0 |D s |
| 689 | 0 | 1 | |a Nichtlineares System |0 (DE-588)4042110-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Nichtlineares System |0 (DE-588)4042110-7 |D s |
| 689 | 1 | 1 | |a Ljapunov-Stabilitätstheorie |0 (DE-588)4167992-1 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Ljapunov-Stabilitätstheorie |0 (DE-588)4167992-1 |D s |
| 689 | 2 | 1 | |a Nichtlineares System |0 (DE-588)4042110-7 |D s |
| 689 | 2 | 2 | |a Vektorwertige Funktion |0 (DE-588)4262911-1 |D s |
| 689 | 2 | |5 DE-604 | |
| 700 | 1 | |a Matrosov, Vladimir M. |e Verfasser |4 aut | |
| 700 | 1 | |a Sivasundaram, S. |e Verfasser |4 aut | |
| 830 | 0 | |a Mathematics and its applications |v 63 |w (DE-604)BV008163334 |9 63 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002904923&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 940 | 1 | |n oe | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-002904923 | |
Record in the Search Index
| _version_ | 1826831280383197185 |
|---|---|
| adam_text |
Contents
Series Editor's Preface v
Preface ix
Chapter 1. Why several Lyapunov functions? 1
1.0. Introduction 1
1.1. Trends in basic Lyapunov theory 2
1.2. Definitions of stability and boundedness 6
1.3. Fundamental comparison of results 12
1.4. Refinements of basic Lyapunov theorems 16
1.5. Boundedness and practical stability 27
1.6. Method of vector Lyapunov functions 32
1.7. Stability concepts in terms of two measures 38
1.8. Practical stability and boundedness 44
1.9. Global results 48
1.10. Notes 52
Chapter 2. Refinements. 53
2.0. Introduction 53
2.1. Perturbed systems 54
2.2. Large scale dynamic systems 58
2.3. A technique in perturbation theory 61
2.4. Quasisolutions 66
2.5. Analysis of comparison systems 69
2.6. Matrix Lyapunov functions 73
2.7. Cone valued Lyapunov functions 75
2.8. Higher derivatives of Lyapunov functions 77
2.9. New directions 81
2.10. Existence and stability of stationary points 88
2.11. Notes 91
Chapter 3. Extensions 93
3.0. Introduction 93
3.1. Differential equations with infinite delay 93
3.2. Integro differential equations of Volterra type 101
viii Contents
3.3. Difference equations 105
3.4. Impulsive differential equations 111
3.5. Reaction diffusion systems 114
3.6. Control systems 119
3.7. Decentralized control systems 123
3.8. Optimal controllability 125
3.9. Set valued differential inequalities 128
3.10. Stability criteria 131
3.11. Notes 133
Chapter 4. Applications 135
4.0. Introduction 135
4.1. Models from economics 135
4.2. Motion of an aircraft 138
4.3. Models in immunology 140
4.4. Models from neural networks 147
4.5. Population models 152
4.6. Models from chemical kinetics 156
4.7. Notes 158
Appendix 159
References 163
Index 171 |
| any_adam_object | 1 |
| author | Lakshmikantham, Vangipuram 1926-2012 Matrosov, Vladimir M. Sivasundaram, S. |
| author_GND | (DE-588)104268050 |
| author_facet | Lakshmikantham, Vangipuram 1926-2012 Matrosov, Vladimir M. Sivasundaram, S. |
| author_role | aut aut aut |
| author_sort | Lakshmikantham, Vangipuram 1926-2012 |
| author_variant | v l vl v m m vm vmm s s ss |
| building | Verbundindex |
| bvnumber | BV004725111 |
| callnumber-first | Q - Science |
| callnumber-label | QA871 |
| callnumber-raw | QA871 |
| callnumber-search | QA871 |
| callnumber-sort | QA 3871 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 520 |
| classification_tum | MAT 345f |
| ctrlnum | (OCoLC)23144362 (DE-599)BVBBV004725111 |
| dewey-full | 003/.75 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 003 - Systems |
| dewey-raw | 003/.75 |
| dewey-search | 003/.75 |
| dewey-sort | 13 275 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 cb4500</leader><controlfield tag="001">BV004725111</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20090810</controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">920226s1991 xx |||| 00||| engod</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0792311523</subfield><subfield code="9">0-7923-1152-3</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)23144362</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV004725111</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA871</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">003/.75</subfield><subfield code="2">20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 520</subfield><subfield code="0">(DE-625)143244:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 345f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Lakshmikantham, Vangipuram</subfield><subfield code="d">1926-2012</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)104268050</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Vector Lyapunov functions and stability analysis of nonlinear systems</subfield><subfield code="c">by V. Lakshmikantham, V. M. Matrosov and S. Sivasundaram</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Dordrecht [u.a.]</subfield><subfield code="b">Kluwer</subfield><subfield code="c">1991</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">X, 172 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Mathematics and its applications</subfield><subfield code="v">63</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Liapounov, fonctions de</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Stabilité</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Théories nonlinéaires</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Lyapunov functions</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Nonlinear theories</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stability</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtlineares System</subfield><subfield code="0">(DE-588)4042110-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Ljapunov-Funktion</subfield><subfield code="0">(DE-588)4274502-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Vektorwertige Funktion</subfield><subfield code="0">(DE-588)4262911-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Ljapunov-Stabilitätstheorie</subfield><subfield code="0">(DE-588)4167992-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Ljapunov-Funktion</subfield><subfield code="0">(DE-588)4274502-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Nichtlineares System</subfield><subfield code="0">(DE-588)4042110-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Nichtlineares System</subfield><subfield code="0">(DE-588)4042110-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Ljapunov-Stabilitätstheorie</subfield><subfield code="0">(DE-588)4167992-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Ljapunov-Stabilitätstheorie</subfield><subfield code="0">(DE-588)4167992-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2="1"><subfield code="a">Nichtlineares System</subfield><subfield code="0">(DE-588)4042110-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2="2"><subfield code="a">Vektorwertige Funktion</subfield><subfield code="0">(DE-588)4262911-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Matrosov, Vladimir M.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Sivasundaram, S.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Mathematics and its applications</subfield><subfield code="v">63</subfield><subfield code="w">(DE-604)BV008163334</subfield><subfield code="9">63</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002904923&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="n">oe</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-002904923</subfield></datafield></record></collection> |
| id | DE-604.BV004725111 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-17T09:01:10Z |
| institution | BVB |
| isbn | 0792311523 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002904923 |
| oclc_num | 23144362 |
| open_access_boolean | |
| owner | DE-12 DE-91G DE-BY-TUM DE-739 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-634 DE-11 DE-188 |
| owner_facet | DE-12 DE-91G DE-BY-TUM DE-739 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-634 DE-11 DE-188 |
| physical | X, 172 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Lakshmikantham, Vangipuram 1926-2012 Verfasser (DE-588)104268050 aut Vector Lyapunov functions and stability analysis of nonlinear systems by V. Lakshmikantham, V. M. Matrosov and S. Sivasundaram Dordrecht [u.a.] Kluwer 1991 X, 172 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 63 Liapounov, fonctions de ram Stabilité ram Théories nonlinéaires ram Lyapunov functions Nonlinear theories Stability Nichtlineares System (DE-588)4042110-7 gnd rswk-swf Ljapunov-Funktion (DE-588)4274502-0 gnd rswk-swf Vektorwertige Funktion (DE-588)4262911-1 gnd rswk-swf Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd rswk-swf Ljapunov-Funktion (DE-588)4274502-0 s Nichtlineares System (DE-588)4042110-7 s DE-604 Ljapunov-Stabilitätstheorie (DE-588)4167992-1 s Vektorwertige Funktion (DE-588)4262911-1 s Matrosov, Vladimir M. Verfasser aut Sivasundaram, S. Verfasser aut Mathematics and its applications 63 (DE-604)BV008163334 63 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002904923&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lakshmikantham, Vangipuram 1926-2012 Matrosov, Vladimir M. Sivasundaram, S. Vector Lyapunov functions and stability analysis of nonlinear systems Mathematics and its applications Liapounov, fonctions de ram Stabilité ram Théories nonlinéaires ram Lyapunov functions Nonlinear theories Stability Nichtlineares System (DE-588)4042110-7 gnd Ljapunov-Funktion (DE-588)4274502-0 gnd Vektorwertige Funktion (DE-588)4262911-1 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd |
| subject_GND | (DE-588)4042110-7 (DE-588)4274502-0 (DE-588)4262911-1 (DE-588)4167992-1 |
| title | Vector Lyapunov functions and stability analysis of nonlinear systems |
| title_auth | Vector Lyapunov functions and stability analysis of nonlinear systems |
| title_exact_search | Vector Lyapunov functions and stability analysis of nonlinear systems |
| title_full | Vector Lyapunov functions and stability analysis of nonlinear systems by V. Lakshmikantham, V. M. Matrosov and S. Sivasundaram |
| title_fullStr | Vector Lyapunov functions and stability analysis of nonlinear systems by V. Lakshmikantham, V. M. Matrosov and S. Sivasundaram |
| title_full_unstemmed | Vector Lyapunov functions and stability analysis of nonlinear systems by V. Lakshmikantham, V. M. Matrosov and S. Sivasundaram |
| title_short | Vector Lyapunov functions and stability analysis of nonlinear systems |
| title_sort | vector lyapunov functions and stability analysis of nonlinear systems |
| topic | Liapounov, fonctions de ram Stabilité ram Théories nonlinéaires ram Lyapunov functions Nonlinear theories Stability Nichtlineares System (DE-588)4042110-7 gnd Ljapunov-Funktion (DE-588)4274502-0 gnd Vektorwertige Funktion (DE-588)4262911-1 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd |
| topic_facet | Liapounov, fonctions de Stabilité Théories nonlinéaires Lyapunov functions Nonlinear theories Stability Nichtlineares System Ljapunov-Funktion Vektorwertige Funktion Ljapunov-Stabilitätstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002904923&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT lakshmikanthamvangipuram vectorlyapunovfunctionsandstabilityanalysisofnonlinearsystems AT matrosovvladimirm vectorlyapunovfunctionsandstabilityanalysisofnonlinearsystems AT sivasundarams vectorlyapunovfunctionsandstabilityanalysisofnonlinearsystems |